"Elevator music" is the general, mildly pejorative term for music that is written or performed with the intention of having the music set the atmosphere or the mood of a place, and be otherwise ignored and not call attention to itself.
It's 'background music', 'dinner music' etc. It's music in the gaseous state.
Real music has a beginning, a structure, a middle, a development, a melody, some variations, a resolution, and an end. 'Elevator music' really doesn't need any of these things. It's built and performed in such a way that its effects on a listener completely DON'T depend on when he comes in, how long he stays, whether he tunes in or tunes out, and when he leaves.
A tremolo is a rapid alternation between two notes (or sets of notes, you can have polyphonic tremolos) which can be any arbitrary distance apart — including zero. A trill is a subset of tremolo, where the distance between any two notes being alternated is a second, either major or minor.